cp's OEIS Frontend

A169418 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.

%I A169418 #14 Jun 05 2019 10:42:14
%S A169418 1,21,420,8400,168000,3360000,67200000,1344000000,26880000000,
%T A169418 537600000000,10752000000000,215040000000000,4300800000000000,
%U A169418 86016000000000000,1720320000000000000,34406400000000000000
%N A169418 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
%C A169418 The initial terms coincide with those of A170740, although the two sequences are eventually different.
%C A169418 First disagreement is at index 32, the difference is 210. - _Klaus Brockhaus_, Jun 27 2011
%C A169418 Computed with Magma using commands similar to those used to compute A154638.
%H A169418 <a href="/index/Rec#order_32">Index entries for linear recurrences with constant coefficients</a>, signature (19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, -190).
%F A169418 G.f.: (t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(190*t^32 - 19*t^31 - 19*t^30 - 19*t^29 - 19*t^28 - 19*t^27 - 19*t^26 - 19*t^25 - 19*t^24 - 19*t^23 - 19*t^22 - 19*t^21 - 19*t^20 - 19*t^19 - 19*t^18 - 19*t^17 - 19*t^16 - 19*t^15 - 19*t^14 - 19*t^13 - 19*t^12 - 19*t^11 - 19*t^10 - 19*t^9 - 19*t^8 - 19*t^7 - 19*t^6 - 19*t^5 - 19*t^4 - 19*t^3 - 19*t^2 - 19*t + 1).
%F A169418 G.f.: (1+2*sum(k=1..31, x^k)+x^32)/(1-19*sum(k=1..31, x^k)+190*x^32).
%t A169418 coxG[{32,190,-19}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jun 05 2019 *)
%Y A169418 Cf. A170740 (G.f.: (1+x)/(1-20*x) ).
%K A169418 nonn
%O A169418 0,2
%A A169418 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009